Facility location (cooperative game)

• There are several consumers who need a certain service, e.g, electricity connection.
• There are several locations where facilities can be built.
• For every pair of consumer and location, there is a fixed cost of serving C from L. This cost is denoted Cost.
• The cost of serving a group of consumers is lower than the sum of the cost of serving each consumer alone.

• There are two facilities, F1 which costs 2 and F2 which costs 2.
• There are three consumers, Alice Bob and Carl.
• Alice can be served only from F1, with cost 2. So the cost of serving her alone is 2+2=4.
• Bob can be served from F1 with cost 2 or from F2 with cost 1. So the cost of serving him alone is 2+1=3.
• Carl can be served only from F2, with cost 1. So the cost of serving him alone is 2+1=3.
• The cost of serving Alice and Bob is 2+2+2=6.
• The cost of serving Bob and Carl is 2+1+1=4.
• The cost of serving Alice and Carl is 2+2+2+1=7.
• The cost of serving all agents is 2+2+2+1+1=8.

• The cost-vector is not in the core, since Alice can deviate and get a cost of only 4. Similarly, the vector is not in the core since Bob and Carl can deviate together and get a total cost of only 4.
• The cost-vectors and are in the core.